Systems of Inequalities: Graphing and Solutions

Front

What is a system of inequalities?

Back

A system of inequalities is a set of two or more inequalities with the same variables. The solution is the set of all points that satisfy all inequalities in the system.

Front

How do you graph a system of inequalities?

Back

To graph a system of inequalities, first graph each inequality as if it were an equation. Then, shade the region that satisfies the inequality. The solution to the system is where the shaded regions overlap.

Front

What does it mean for a point to be a solution to a system of inequalities?

Back

A point is a solution to a system of inequalities if it satisfies all inequalities in the system, meaning it lies in the overlapping shaded region of the graph.

Front

What is the difference between a solid line and a dashed line in graphing inequalities?

Back

A solid line indicates that the points on the line are included in the solution (≥ or ≤), while a dashed line indicates that the points on the line are not included (> or <).

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How do you determine if a point is a solution to an inequality?

Back

To determine if a point is a solution to an inequality, substitute the x and y values of the point into the inequality. If the inequality holds true, then the point is a solution.

Front

What is the graphical representation of the inequality y < 2x + 3?

Back

The graph of y < 2x + 3 is a dashed line with a slope of 2 and a y-intercept of 3, with the area below the line shaded.

Front

What does the solution set of a system of inequalities represent?

Back

The solution set of a system of inequalities represents all the possible solutions that satisfy all inequalities in the system, typically shown as a shaded region on a graph.

Front

How can you identify the correct graph for a given inequality?

Back

To identify the correct graph for a given inequality, look for the line that corresponds to the equation and check the shading direction based on the inequality sign.

Front

What is the significance of the intersection of shaded regions in a system of inequalities?

Back

The intersection of shaded regions in a system of inequalities represents the set of all points that satisfy all inequalities in the system.

Front

What is the slope-intercept form of a linear inequality?

Back

The slope-intercept form of a linear inequality is written as y = mx + b, where m is the slope and b is the y-intercept, with an inequality sign (>, <, ≥, ≤) instead of an equals sign.